Abstract
We simulate the flow of a yield stress fluid around a gas bubble using an augmented Lagrangian approach with piecewise linear equal-order finite elements for both the velocity and the pressure approximations. An enhanced mesh adaptive strategy based on this element-pair choice is also proposed to render the yield surfaces with desired resolution. The corresponding numerical scheme is formulated for general Herschel–Bulkley fluids. Numerical results on Bingham fluid flows around a slowly rising spherical gas bubble are provided to showcase the improvement on the previously proposed algorithm in (Zhang, Int J Numer Methods Fluids 69:731–746, 2012).
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Acknowledgments
The author would like to thank Dr. I. Frigaard for valuable discussions and suggestions during her stay as a postdoctoral researcher at the University of British Columbia. The author is also grateful for Dr. D. Vola’s generous help with some implementation issues on the related numerical algorithm.
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Zhang, J. (2016). An Augmented Lagrangian Approach with Enhanced Local Refinement to Simulating Yield Stress Fluid Flows Around a Spherical Gas Bubble. In: Chen, K., Ravindran, A. (eds) Forging Connections between Computational Mathematics and Computational Geometry. Springer Proceedings in Mathematics & Statistics, vol 124. Springer, Cham. https://doi.org/10.5176/2251-1911_CMCGS14.04_1
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DOI: https://doi.org/10.5176/2251-1911_CMCGS14.04_1
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16138-9
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